# Full text of "Treatise On Analysis Vol-Ii"

## See other formats

```448       INDEX

Cauchy-Schwarz inequality: 13.11

Cauchy's determinant: 13.11, prob. 6

Cay ley transform of a hermit ian operator:

15.13

Centralizer of a subset of a group: 12.8
Chacon-Ornstein ergodic theorem: 13.17,

prob. 5

Chaotic topology: 12.1
Character of an algebra: 15.3
Characteristic function of a set: 12.7
Choquet's theorem: 13.10, prob. 8
ChristofTel-Darboux formula: 15.13, prob. 3
Closed convex hull: 12.14, prob. 13
Closed graph theorem: 12.16
Closed unbounded operator: 15.12
Closure of an unbounded operator: 15.12
Coarser covering: 12.6
Coarser partition: 13.9, prob. 7
Coarser topology: 12.1
Compact space: 12.2 and 12.3, prob. 6
Comparable topologies, 12.1
Compatible (topology and group structure):

12.8
Compatible  (topology and  vector  space

structure): 12.13
Complete maximum principle: 13.13,

prob. 2

Complex measure: 13.1
Compressible mapping: 13.9, prob. 11
Condensation of singularities: 12.16, prob.

14

Conjugacy: 15.13, prob. 7
Conjugate of a complex measure: 13.2
Conjugate mappings preserving a measure:

13.12, prob. 11

Continued fraction: 13.14, prob. 4
Continuous almost everywhere: 13.9,

prob. 6

Convergence in mean, in square mean: 13.11
Convergence in measure: 13.2, prob. 2
Convergents to a continued fraction: 13.14,

prob. 4

Convex hull: 12.14, prob. 13
Convolution of a measure and a function-

14.8

Convolution of two measures: 14.5
Convolvable function and measure: 14.8
Convolvable functions: 14.10
Convolvable measures: 14.5

Cotlar's lemma: 15.4, prob. 16
Covering (G-): 14.1, prob. 6

Defect of an unbounded hermitian operator:
15.13

Defined almost everywhere: 13.6

Dense point, with respect to a measure-
preserving transformation: 13.11, prob.
11.

Density with respect to a measure: 13.1 and
13.13

Differentiation under the integral sign: 13.8

Diffuse measure: 13.18

Dirac measure: 13.1

Directed set of seminorms: 12.14

Dirichlet algebra: 15.3, prob. 9

Dirichlet series: 12.7, prob. 9

Discrete topology: 12.1

Disjoint measures: 13.18

Domain of an unbounded operator: 15.12

Dominated convergence theorem: 13.8

Dual of a locally convex space: 12.15

Dunford-Schwartz ergodic theorem: 13.21,
prob. 20

Egoroff's theorem: 13.9

Elementary set: 12.5

Entropy: 13.9, probs. 27, 28

Equi-integrable set: 13.12, prob. 4

Equirepartitioned sequence: 13.4, prob. 7

Equivalent functions: 13.6

Equivalent measures: 13.15

Equivalent representations: 15.5

Equivalent seminorms: 12.14

Ergodic mapping, measure: 13.9, prob. 13

Ergodic point, with respect to a measure-
preserving transformation: 13.11, prob.
11

Ergodic set: 13.11, prob. 11

Essential spectrum: 15.13, prob. 11

Essential subspace: 15.5

Essentially bounded function: 13.12